A right triangle △ABC with right angle C is inscribed in a circle. Find the radius of this circle if: Given m∠C = 90°, k(O, r) inscribed in △ABC, AC = 8 cm, BC = 6 cm. Find r.

Answer:

Yep! an open dot is <

A closed dot means ≤

Hope this helps! :)

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For this case we have that the equation of the line of the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have as data that:

[tex]m = \frac {1} {4}\\b = - \frac {3} {4}[/tex]

Substituting:

[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]

Answer:

[tex]y = \frac {1} {4} x- \frac {3} {4}[/tex]

Answer: I'm pretty sure its 1562

Answer:

The sum of 22 terms of given AP = 1562

Step-by-step explanation:

Formula:-

Sum of n terms of AP,

Sₙ= (n/2)[2a + (n - 1)d]

To find the sum of 22 terms

Here. a = 8, d = 6 and n = 22

Sₙ= (n/2)[2a + (n - 1)d]

S₂₂ = (22/2)[2*8 + (22 - 1)*6]

  = 11[16 + 126] = 11 * 142 = 1562

The solution of the expression (a-b)²/{(1/a)-(1/b)} is ab² - a²b.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An expression,

(a-b)²/{(1/a)-(1/b)}.

Simplifying,

(a-b)²/{(1/a)-(1/b)},

= (a-b)²/{(b-a)/ab},

= -(a-b)² (ab)/(a-b)

= -(a-b)(ab)

= ab² - a²b.

Therefore,  ab² - a²b is the solution.

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Final answer:

The expression (a-b)²/(1/a-1/b) simplifies by first finding a common denominator, then multiplying to remove the fraction, resulting in the simplified form -ab(a-b).

Explanation:

To simplify the expression (a-b)²/(1/a-1/b), we can start by finding a common denominator for the terms in the denominator 1/a and 1/b. The common denominator is a × b, so we rewrite the expression as:

((a-b)²) / ((b - a) / (ab))

Now, we can simplify by multiplying both the numerator and the denominator by ab to eliminate the fraction in the denominator:

(a-b)² × (ab) / (b - a)

Note that (a - b) is equal to -(b - a), so:

(a-b)² × (ab) / -(a - b)

Because (a - b)² is (a - b) × (a - b), one (a - b) in the numerator cancels with the (a - b) in the denominator, leaving us with:

-(a - b) × (ab)

Which simplifies to:

-ab(a - b)

ANSWER

[tex]a_{34} = 8[/tex]

EXPLANATION

The given matrix is a 4 by 4 matrix.

The entry in the intersection of the first third row and the fourth column is denoted

[tex]a_{34}[/tex]

This entry is 8.

Check the attachment for how we got the 8.

Therefore

[tex]a_{34} = 8[/tex]

ANSWER

The range is

{-1,0,1,3,4,5}

EXPLANATION

The relation is given to us as an ordered pair.

The range is the set of all the y-values of the relation.

We list the set of all the values in ascending order without any repetition.

We then obtain the range as:

{-1,0,1,3,4,5}

Answer:

{1,2,3,7}

Step-by-step explanation:

The range of a relation is the set of y-values of the ordered pairs.

The given relation is:

ƒ={(5, 1),(6, 2),(7, 3),(8, 1),(9, 7)},

The set of y-values of the given ordered pairs are;

{1,2,3,7}

Therefore the range of y is {1,2,3,7}

Answer:

{[tex]1, 2, 3, 7[/tex]}

Step-by-step explanation:

Imagine fucntions as little machines that turn one number into another. The numbers that enter are called domain and the numbers that go out are called range. In this excercise we are given the couples of numbers that go in and out of the machine. Like this:

[tex](NumberIn,NumberOut)[/tex]

So the range of this function will be all the number going out of the function

(NumberOut) and this are:

{[tex]1, 2, 3, 7[/tex]}

Answer:

9

Step-by-step explanation:

when u add her past five scored together, you get 39. your equation would be

39 + x

-------------         = 8

6

you multiply both sides by 6 and get

39+x = 48

subtract 39 from both sides to get 9

Answer:

2,008,747,295,829,492‬

Step-by-step explanation:

2008747295829492= 1000 + 2008747295828492

Answer:

pictures 1, 2, 4, and 6

Step-by-step explanation:

Answer:

8 units

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 1, - 5) and (x₂, y₂ ) = (- 9, - 5)

d = [tex]\sqrt{(-9+1)^2+(-5+5)^2}[/tex]

  = [tex]\sqrt{(-8)^2+0^2}[/tex]

  = [tex]\sqrt{64}[/tex]

  = 8 units

Explanation:

15. x = 148°, z = 32°

In a parallelogram, adjacent angles are supplementary, so must add to 180°. That also means opposite angles are congruent.

___

17. x = 8, y = -3

The diagonals bisect each other, so ...

2x -4 = 12

x = (12 +4)/2 = 8

and ...

y +10 = 7

y = 7 -10 = -3

__

21. The diagonals of a parallelogram bisect each other, so their point of intersection is their midpoint. The midpoint of WY can be computed as ...

P = (W+Y)/2 = ((-3, 5) +(3, 1))/2 = (0, 6)/2 = (0, 3)

The diagonals intersect at (0, 3).

Final answer:

The expression to verify that g(x) is the inverse of f(x) is to check if f(g(x)) = x and g(f(x)) = x. When we calculate both expressions for the given functions, they both simplify to x, which confirms that g(x) is the inverse of f(x).

Explanation:

To verify that g(x) is the inverse of f(x), we need to show that composing f with g yields the identity function. In other words, f(g(x)) should equal x, and vice versa, g(f(x)) should also equal x. For the given functions, f(x) = 5x - 25 and g(x) = 1/5x + 5, let's compute f(g(x)) and g(f(x)).

To find f(g(x)), we substitute g(x) into f(x):

f(g(x)) = f(1/5x + 5) = 5(1/5x + 5) - 25 = x + 25 - 25 = x

Next, to find g(f(x)), we substitute f(x) into g(x):

g(f(x)) = g(5x - 25) = 1/5(5x - 25) + 5 = x - 5 + 5 = x

Since both f(g(x)) and g(f(x)) equal x, we can conclude that g(x) is indeed the inverse of f(x).

Answer : x^1/2 y -1/3/x^/4 cdot y^1/2= y^1/3

Step-by-step explanation: Hope this helps !!!

Plz give me 5 star & thanks! :}

Okay so in this question it says to solve f(7). This means to plug in the 7 every where you see an x, so that it looks like this: [tex]\frac{3}{7+2} -\sqrt{7-3}[/tex]Then you'll solve it like a normal equation.

Hope this helped! Let me know if there is anything I need to clarify or explain more in depth!

Answer:

- 1.67

Step-by-step explanation:

To evaluate f(7) substitute x = 7 into the expression

f(7) = [tex]\frac{3}{7+2}[/tex] - [tex]\sqrt{7-3}[/tex]

     = [tex]\frac{3}{9}[/tex] - [tex]\sqrt{4}[/tex]

     = [tex]\frac{1}{3}[/tex] - 2

     = [tex]\frac{1}{3}[/tex] - [tex]\frac{6}{3}[/tex]

     = - [tex]\frac{5}{3}[/tex] ≈ - 1.67

Point c.

You can graph the two points in a calculator to find out the answer OR you can identify the lines using the y-intercept aka b in the y=mx+b format.

Y=x - 3 has a y-intercept of -3, so look for the line where it goes through -3 on the y axis. (do the same for the other except when the y-intercept is 1)

From this, you can identify the lines and just find where they intersect.

Answer:

CCCCCCCCCCCCCC

Step-by-step explanation:

Answer:

The diameter of the rug is [tex]4\ ft[/tex]

Step-by-step explanation:

we know that

The circumference of a circle (circular rug) is equal to

[tex]C=\pi D[/tex]

where

D is the diameter of the circle

In this problem we have

[tex]C=12.56\ ft[/tex]

substitute in the formula and solve for D

[tex]12.56=(3.14)D[/tex]

[tex]D=12.56/(3.14)=4\ ft[/tex]

Answer:

$11.00

Explanation:

$60 given - $49 order = $11 change

Answer:

It's 11 because 60-49 equals 11.

Step-by-step explanation:

Inscribed angles are pretty easy, they're always half the corresponding central angle.  The arc measure are always of central angles.

1. We're told to arc is 62 degrees so the inscribed angle is half,

WXY = 31 degrees.

2. Here we're told the inscribed angle is 113 degrees so the arc is double,

DGF=226 degrees

3. Angles which subtend a diameter are always right angles.

PQR = 90 degrees

4. If we draw DC we see it's a radius too, so DC=DB and we have an isosceles triangle so DCB=47 degrees so BDC=180-47-47=86.  The central angle is the arc measure so

BC=86 degrees

5. Angle JNK=53 degrees and angles NJK=NKJ because we have an isosceles triangle, two sides radii.  So NKJ=(180-53)/2.

Similarly NKL=(180-65)/2

So angle JKL=NKJ+NKL=180 - (65+53)/2 = 180 - 118/2 = 121 degrees

I better leave the rest for you.

An inscribed angle is formed by two secant lines intersecting on a circle's circumference and is half the measure of the central angle intercepting the same arc. Fundamental theorems like the Pythagorean theorem and mnemonic SOHCAHTOA are important in geometry, especially when dealing with circles and triangles.

An inscribed angle is formed when two secant lines of a circle intersect on the circle's circumference. The value of an inscribed angle is always half the measure of the central angle that intercepts the same arc.

This is a foundational concept in geometry that is often linked to other geometric properties and theorems, such as the relationship between angles and arcs, and the behavior of angles within and outside of circles.

Knowing how to work with inscribed angles is crucial, particularly when dealing with problems involving circles.

For example, if you know the measure of the central angle, you can easily find the inscribed angle by dividing the central angle by 2. Recall other basic geometrical facts, such as the Pythagorean theorem, which states that in a right triangle, a² + b² = c² (where c is the hypotenuse), and the mnemonic SOHCAHTOA which helps remember the relationships of sides and angles in right triangles.

To help visualize these concepts, sketching triangles and remembering that the angles of a triangle sum up to 180 degrees can be helpful. Plane geometry forms the basis for understanding these principles, which is essential in tackling more advanced problems in circles and other geometric figures.

Answer:

9.9 x 10.1 x 10.0

Step-by-step explanation:

9.9 x 10.1 x 10.0 = 999.9 ft3

This the closest to the true known value.

Other answers mat be more precise, but not as accurate.

Accuracy is how close a measured value is to the actual or true value.

Cheers

Answer:

A)

Step-by-step explanation:

Here are the choices:

A) 9.9 x 10.1 x 10.0

B) 9.91 x 10.11 x 10.00

C) 9.911 x 10.112 x 10.002

D) 9.9113 x 10.1125 x 10.0028

Here are the volumes produced by each choice of measures.

A) 999.9

B) 1001.9

C) 1002.4

D) 1002.56

Answer: A) since the volume os colsest to the real volume.

Answer:

Each team recieved $312

Step-by-step explanation:

You will take $5145 - 777 = 4368 which is the balance

4368 of the balance  ÷ 14 teams =312

each team received  $312

After paying the expenses of $777 from the fund-raising total of $5145, $4368 was left. When this amount was divided evenly amongst 14 soccer teams, each team received $312.

To solve the problem, we first need to subtract the expenses from the total fund-raising amount. This gives us $5145 - $777 = $4368.

After the expenses are taken into consideration, the remaining money is divided evenly among the 14 soccer teams. This is calculated by taking the remaining money and dividing it by the number of teams, $4368 ÷ 14 = $312.

So, each team will receive $312 after all the expenses are paid.

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Answer:

Corresponding angles theorem.

Step-by-step explanation:

The corresponding angles theorem states that corresponding angles are congruent.

Pretty much means that every other angle is congruent if two lines are parallel and a line traverses them.

Answer: angle 2 and angle 6 are both corresponding angles

Step-by-step explanation:

If the two angles are matching corners, they are corresponding to one another. Hope this helps and have a good day:)

Answer:

11/12

Step-by-step explanation:

1/4+2/3

1/4×3/3+2/3×4/4

3/12+8/12

[tex]\boxed{R_{4}=20\Omega}[/tex]

If resistors are in series, so the current  [tex]I[/tex] is the same in all of them. In this problem we have four resistors. So, we can get a relationship between the Equivalent resistance  of series combination and the four resistors as follows:

[tex]R_{eq}=R_{1}+R_{2}+R_{3}+R_{4}[/tex]

[tex]R_{eq}[/tex] is the total resistance [tex]50\Omega[/tex]. Moreover:

[tex]R_{1}=5\Omega \\ R_{2}=10\Omega \\ R_{3}=15\Omega[/tex]

Therefore:

[tex]50=5+10+15+R_{4} \\ \\ R_{4}=50-(5+10+15) \\ \\ R_{4}=50-30 \\ \\ \boxed{R_{4}=20\Omega}[/tex]

Answer:

x = 3 is a true solution.

The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.

Step-by-step explanation:

Given in the question an equation,

√(x-2) - 4 = x - 6

√(x-2) = x - 6 + 4

√(x-2) = x -2

Take square on both sides of the equation

√(x-2)² = (x -2)²

x - 2 = x² - 4x + 4

0 = x² - 4x - x + 4 + 2

0  = x² - 5x + 6

a = 1

b = -5

c = 6

x = -b±√(b²-4ac) / 2a

x = -(-5)±√(5²-4(1)(6)) / 2(1)

x = 5 ± √1 / 2

x = 5 + 1 / 2 or  5 - 1 /2

x = 3 or x = 2

Plug value of x in the radical equation:

√(3-2)-4=3-6

√1 -4 = -3

 1 - 4 = -3

    -3 = -3

√(2-2)-4=2-6

0 - 4 = -4

    -4 = -4

Answer:

C. x = 3 is a true solution.

E. The zeros of 0 = x2 – 5x + 6 are possible solutions to the radical equation.

Step-by-step explanation:

Answer:

option A

(1.5,1.2)

Step-by-step explanation:

Given in the question two equations

Equation 1

y = √x

Equation 2

y = x²- 1

Equate both equations

√x = x²- 1

We can see from the graph that both meets when x =  1.5 and y = 1.2

we can plug the options given one by one to see which points satisfy

one thing we know is that x ≠ any negative value since

y = √x and square root of negative value is not possible

so option b and c are rejected

  option A

√1.5 = y = 1.2

1.5²- 1 = y = 1.2

Answer:

Im pretty sure he got 24

Step-by-step explanation:

Because if you divide 12.30 by .50 you get 24.6 and the 6 could mean sales tax and other stuff

Answer:

29

Step-by-step explanation:

the rule PEMDAS means first use the parentheses, (  ,  )

so order of operation, first you do parentheses, 20/4=5 then 5-5=0

so that is the parentheses now take core of stuff outside of parentheses and    29 x 1=29

P= parentheses

E = Exponents

M= multiply

D = divide

A= addition

S= subtract

also know as order of operation!

hope this helps. please mark brainliest! have a good day

The value of expression 29 • 1 + 2(20 ÷ 4 – 5)= 29

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

To solve the given expression we will use:

The PEMDAS rule means

P= Parentheses

E = Exponents

M= multiply

D = divide

A= addition

S= subtract

first we do parentheses,

29 • 1 + 2(20 ÷ 4 – 5)= 29.1+2(5-5)

                                  = 29.1+2(0)

                                  = 29.1+0

                                 =29

Thus,  29 • 1 + 2(20 ÷ 4 – 5)  =29

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Answer:

Part 1) The lateral area is [tex]LA=791.7\ ft^{2}[/tex]

Part 2) The surface area is  [tex]SA=1,244.1\ ft^{2}[/tex]

[tex]LA=791.7\ ft^{2}[/tex], [tex]SA=1,244.1\ ft^{2}[/tex]

Step-by-step explanation:

step 1

Find the lateral area of the cone

we know that

The lateral area of the cone is equal to

[tex]LA=\pi rl[/tex]

we have

[tex]r=12\ ft[/tex]

[tex]l=21\ ft[/tex]

substitute

[tex]LA=(3.1416)(12)(21)=791.7\ ft^{2}[/tex]

step 2

Find the surface area of the cone

we know that

The surface  area of the cone is equal to

[tex]SA=\pi r^{2}+LA[/tex]

we have

[tex]r=12\ ft[/tex]

[tex]LA=791.7\ ft^{2}[/tex]

substitute

[tex]SA=(3.1416)(12)^{2}+791.7=1,244.1\ ft^{2}[/tex]

Final answer:

Tipping a fortune teller involves giving them a gratuity as a gesture of appreciation for their service.

Explanation:

When you tip a fortune teller, you are giving them a gratuity or extra money as a gesture of appreciation for their service. Tipping is a common practice in various service industries, including fortune-telling. It is a way to show gratitude for the insights or entertainment provided by the fortune teller.